Tolkien spent a life on the world "behind" The Lord of the Rings. Almost literally. I daresay it's hard he can have used even a small fraction of his "energy" and time in order to create other worlds which can compare to a fraction of the amount of details and depth of his Middle Earth or even have just the bare minimum to be considered "large works" or "worlds" and not only as "scenery" or "setting" for a tale.
This is, as pretended it should be by DVK, a quantative analysis made by heart on what I've read of and on JRRT. JRRT mind was so much "into" his world that he was able to answer to curious letters asking about flowers, trees, and other details which even are not showing off in published books, as if he was talking about a real, existing world.
Who has his creative mind so deeply "engaged" in such a great creation, hardly create things that diverge enough and yet can be considered "world", and that are large works, unless you want to count a generic "setting" for a tale.
But then, every writer creates a "world" in the very moment he writes or draws something — even I did it several times, even when in my youth I've painted a section (like an anthill in a glass box) of an underearth network of tunnels where humans took refuge from monsters. And about JRRT, yes he wrote (or drew) "stuffs" which are not part of "The World", and so they have their own setting, and a tale (or collection of tales) setting could be counted as a world of its own.
But if you follow this as definition for a "world", then the answer is Yes of course, since he wrote other tales somewhat unrelated to "The World", and, according to the balancedmama answer words (bold is mine):
at least as complete as the standard story "world."
Since I do not count any of the works of the "balanced mama" answer as world, nor as large works, (nor I count as "world" the settings of standard stories), then my answer to this question continue to be no, JRRT has not created other worlds beyond "The World".
It seems like the OP has relaxed his vague requirements of large works or fleshed-out worlds, since there's no discussion about what these requirements should be actually, and whether the other works of JRRT fulfil them.
There are first general questions about what is a «large work», and what is a «flashed-out world». Without an agreement on these, every answer could be considered questionable.
Then, what is a large work? How do we evaluate the “largeness” of a work? Is it about the number of pages the author published when he was alive? Is it about the number of published and unpublished pages and notes? Is it about the time spent thinking about the story?… We need to restrict to a measurable (and cognizable) rule. Number of pages or words are measurable, but once we do it, we need to put a landmark somewhere and say, arbitrarily, that everything "before" this landmark is not a «large work», everything "after" is a «large work».
I won't try for real to do such a silly measurement and I will simply claim that none of the other original works of JRRT can be considered «large works». This is surely true if we compare them to his most known creation; but my claim is that it is true in general: there are no stand alone tales which are both «large work» and which are not tied into Arda and Middle Earth.
Now, we have to think about fleshed-out worlds. Since english is not my mother tongue, I had to check the meaning of fleshed-out. It seems to me the requirements is about whether we can consider these worlds detailed enough to be more than simply a "setting" for a story.
But again, how can we measure the amount of “details”? Namely, we need a way to decide if something is a fleshed-out world or it is not.
However, we should first discuss about what we mean by the word “world”. If we use this term in the widest meaning, then —since every tale "happens" somewhere— every tale has its world, and the author of such a tale had to conceive it in order to set his/her story.
That is, if we cancel the adjective fleshed-out, every tale (story, book, …), no matter who's its author, implies a conception of a world —even when it "overlaps" (wholly or partly) with the world we live in; though I think many are thinking implicitly of worlds that are “invention” and therefore would not consider as “worlds” those of, say, the novels by Patricia Conway, or of verist novels.
Once we introduce back the adjective (fleshed-out), we are also back to our original problem: "how much" the world need to be “fleshed-out” in order to be counted for the OP's question?
It is ridicolous to me any appeal to objectivity, since the question has many (if not all) subjective traits. It's equally ridicolous to pretend we need to put the full list of JRRT works, or to do a "quantitative analysis" —provided we have a proper definition of what a "quantitative analysis" is, and we agree upon.
It is a reasonable, but debatable, approach to use the very same thought of JRRT to discuss fairy-stories, provided there's a staid and someway learned intention to do so, but only once we agree that such an interesting discussion would answer the question —rather, I think it can't bring to anything but the arrogant claim to be able to deduce what JRRT would have answered if asked with such a question.
There's a subtle point here. Briefly, using JRRT's own words and thoughts (e.g. about fairy-stories) to show something about a question on JRRT works, does not make the arguments stronger: it would be the same if we would have used words and thoughts of, say, C.S.Lewis, or a literary critic. Unless the OP is asking us to report the answer of the author on his own work —and if he hasn't stated it clearly and directly as answer to a similar question, then we are again in the path of the arrogant claim I was talking about in the previous paragraph.
Therefore, since we must stay in the Land of Speculation and Subjectivity, I prefer to stay also with my own subjectivity —which, by the way, may be, among other things, a consequence of all the readings I've done in my life, included JRRT's writings.
In order to make me consider (a set of) a tale(s), a book(s), a novel(s), … as a «fleshed-out world», I need at least two "elements":
- Maps of the world or part of it (bonus: the maps are produced inside by past or present characters, even if they do not appear in the story; i.e. they are not only an "extra-diegetic" guide given by the author for the reader)
- Language: inhabitants of this world must have a language (or more languages) of their own and this language must prented to exist beyond the few words or sentences the author has used here and there in the tale; namely, the reader must think such a language exists and that the author is able to cook other sentences using a dictionary and a grammar (bonus: the author has really created a language…)
Now, none of the other works I know about (among these, many of those cited in the other answer) have this two "elements" and are not in relationship to «the world of Arda» or LotR.
Thus, my conclusion is that JRRT has not conceived other works that can be considered «large works» or «fleshed-out worlds» beyond the most famous and known "World".
If we relax the constraints, it seems to me the question collapses into this one: has J.R.R.Tolkien written (not necessarily published) other tales/stories/books «that don't have any connection to the world of Arda»?
The answer to this question, as can be easily checked even on the JRRT page on wikipedia, is Yes, he did.